On Oct 4, 2010, at 12:41 PM, John Ragle wrote: > I must be missing something here. How can one expect high fidelity audio > (e.g. 20 HZ to 20 kHz) with a receiver with a pass-band of 2.5 or 3.0 > kHz? > > With those strictures, one is always going to get "carbon mike" or > slightly better audio, no?
No. The data rate through a channel depends not just on the analog bandwidth of a channel, but also the SNR of the channel. See the section "The Capacity of a Continuous Channel" in Part IV (Continuous Channel) in Shannon's 1948 BSTJ paper: http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf Channel capacity in bits/sec is equal to W, the bandwidth, multiplied by the log(base 2) of the (S+N)/N ratio. With appropriate modulation and error correction coding, [Shannon shows that] you can transmit a digital signal, with *any* arbitrarily small, non-zero error bound that you wish to set, at a data rate up to the channel capacity. E.g., Consider a 3 kHz wide channel with (S+N) to N ratio of 30 dB. The power ratio is 1000, thus log2 is 9.96 [2 to the power of 10 = 1024, so log2(1000) is just under 10]. With appropriate modulation and coding, from Shannon, you can potentially get almost 30 kbits/sec of digital data through such a channel. A practical modem from the 1980s can do 28.8 and 33.6 kbits/second through a 3 kHz telephone circuit. The 56 kbits/sec modems achieve the higher rate by using source coding in addition to channel coding, but they cannot maintain 56 kb/s with completely random binary data. Today's DSL modems can do even better (much better), but they depend on the landline's capability to send, albeit attenuated, signals beyond the 3 kHz voice band. Off Topic: You can perhaps understand why some of us revere Claude Shannon much more than we do Albert Einstein :-). http://en.wikipedia.org/wiki/Claude_Shannon The above Wiki article also refers to Shannon's Master's thesis which connected relay circuits with Boolean Algebra -- making it possible to talk about AND gates and OR gates. David Huffman, also in a Master's thesis, added the memory element (what we call flip-flops today). The combination is what makes it possible for me to type this and for you to read it :-). 73 Chen, W7AY ______________________________________________________________ Elecraft mailing list Home: http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/mmfaq.htm Post: mailto:Elecraft@mailman.qth.net This list hosted by: http://www.qsl.net Please help support this email list: http://www.qsl.net/donate.html
